References to "York" are incorrect through this whole story-line. When this was set, York would have been known as Ebacorum (Roman name) or more likely, Eoforwic (Anglian name). When the Vikings conquered Eoforwic they renamed it Jorvik, from which the name York was derived much later. The name York, explicitly spelled that way, was not used until the 13th Century.
The phrase "The king is dead. Long live the king" was not used until the late 13th century, which is many centuries after the events and stories depicted in the series.